Common Core State Standards Content Area: Mathematics Grade Level: Grade 8 Domain: Expressions and Equations Cluster: Work with radicals and integer exponents. Standard: 1, 3, 4
1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^-5 = 3^-3 = 1/3^3 = 1/27
3. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is smaller than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.
4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g.,use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
What understandings are desired?
Students will understand that:(U)
• exponents can be used to express numerical values in different, but equivalent, ways
• scientific notation is used/can be used to represent large and small quantities.
• scientific notation has real-world applications
What essential questions will be considered?
Essential Questions:(Q)
• How can we use exponents to express numerical values in different, but equivalent, ways?
• How and why is scientific notation used to represent very large or very small values?
• How is scientific notation applied in the real world?
What key knowledge and skills will students acquire as a result of this unit?
Students will know:(K)
Students will be able to:(S)
• Definitions: Exponents, scientific notation, powers, standard notation,
decimals, integers
• Critical Details: Properties of exponents, place value, negative, exponents,
scientific notation operations, magnitude, measurements and units.
• Applications: Real world use of scientific notation, problem
solving strategies, data analysis, finding rates.
• demonstrate how to convert numbers expressed as decimals to scientific notation and vice-versa.
• represent large and small quantities using scientific notation.
• solve problems involving scientific notation.
• analyze data that contains scientific notation.
• relate real numbers to their exponential form
• recognize when, and how, to use the properties of exponents.
Stage 1 - Identify Desired Results
Content Area: Mathematics
Grade Level: Grade 8
Domain: Expressions and Equations
Cluster: Work with radicals and integer exponents.
Standard: 1, 3, 4
1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^-5 = 3^-3 = 1/3^3 = 1/27
3. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is smaller than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.
4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g.,use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
What understandings are desired?
• scientific notation is used/can be used to represent large and small quantities.
• scientific notation has real-world applications
What essential questions will be considered?
• How and why is scientific notation used to represent very large or very small values?
• How is scientific notation applied in the real world?
What key knowledge and skills will students acquire as a result of this unit?
decimals, integers
• Critical Details: Properties of exponents, place value, negative, exponents,
scientific notation operations, magnitude, measurements and units.
• Applications: Real world use of scientific notation, problem
solving strategies, data analysis, finding rates.
• represent large and small quantities using scientific notation.
• solve problems involving scientific notation.
• analyze data that contains scientific notation.
• relate real numbers to their exponential form
• recognize when, and how, to use the properties of exponents.
2004 ASCD and Grant Wiggins and Jay McTighe.